Symmetrically shaped reflector antennas are known in the art. Due to the symmetry of axially symmetric reflector antennas, the feed horn pointing direction is along the symmetry axis of the reflector. An axially symmetric low gain reflector antenna such as an earth cover antenna is mechanically stable, but requires a high-power amplifier such as a traveling wave tube to provide enough system gain. A high-gain axially symmetric parabolic reflector antenna, while very compact in size, significantly reduces the power requirement, so that a relatively low power solid state power amplifier can be used instead. But an axially symmetric high-gain antenna requires a two-axis gimbal steering system that leads to a large mechanical movement volume. In order to accommodate the latter in space flight applications, the antenna is typically mounted on a boom to keep it away from the spacecraft, which further compromises mechanical stability. The two-axis gimbal steering mechanism and boom can be reduced to a more stable single rotation axis turntable by special shaping of the reflector, a technique also known in the art. The shaped reflector is kept symmetric with at least one plane of symmetry. Axially symmetric reflector antennas also suffer from aperture blockage, since the feed is at the center of the antenna aperture. High-gain, offset feed, reflector antennas, also well known in the art, solve the aperture blockage problem. In a high-gain, offset feed, shaped reflector, the offset feed horn is tilted in the shaped reflector symmetry plane. However, tilting the offset feed horn only in the shaped reflector symmetry plane can lead to relatively large reflector geometries. Large reflector antenna geometries are not suited for space applications due to strict limitations on weight and the limited available physical space on a spacecraft. What is needed is a new and improved antenna that eliminates the disadvantages of the aforementioned conventional antenna systems.